The optimal value of the CPOMDP problem (P2), \(\bar{C}_{\pi ^\star _{\mathrm {R}}}\) , and the optimal value of the POMDP problem (P3), \(\mathcal {L}^\star ({\mu })\) , ensures the following relation [1]}
\(\bar{C}_{\pi ^\star _{\mathrm {R}}} = \textstyle \sup _{\mu \ge 0}{\mathcal {L}}^\star ({\mu }).\) 
